Mr and Mrs Carson had written to Dr Coleman asking why the air force was the only body to investigate the crash. They wanted to know why there was no external inquiry into the crash, citing the Occupational Safety and Health investigations done by the Department of Labour.
The letter was in contrast to a briefing given two months earlier to the Chief of Air Force, Air Vice-Marshal Peter Stockwell, and the Chief of Defence, Lieutenant General Rhys Jones.
The senior military officers were preparing to address media on December 15 over the findings of the Court of Inquiry into the Anzac Day crash. The notes prepared to assist in responding to media questions included being quizzed about the air force handling the investigation without external involvement.
The "backpocket questions" stated it was possible external investigations would be carried out. "Police might yet examine this from a criminal aspect and (Department) of Labour - OSH - could still seek to investigate."
On February 12, Dr Coleman told the Carsons "the Department of Labour does not investigate events involving the operation of aircraft".
A spokesman for NZ Defence Force said the letter from Dr Coleman was originally written by its own staff.
The spokesman said the draft letter - which contained accurate details - was sent to the Department of Labour for review. He said department staff contradicted the defence view and made changes that ultimately misinformed the Carsons. They included in the letter details saying the Civil Aviation Authority did aircraft inquiries and because the crash was military it would not be involved.
Dr Coleman assured the Carsons the air force systems were capable of fully investigating the crash.
A review by the Crown Law Office later found the Department of Labour was wrong.
A spokesman for Dr Coleman confirmed the minister had not contacted the Carsons to explain the error. He said the new Ministry of Business, Innovation and Employment had met the Carsons to explain the Department of Labour had misunderstood the law.